This invention generally relates to modeling or analyzing electrical circuit elements such as inductors and/or transformers so that their electrical characteristics and/or equivalent circuit parameters may be determined. The invention herein also relates to simulating the performance of electronic circuits incorporating such elements. Further, the invention relates to modeling inductors and/or transformers using a computer aided design system to facilitate design of practical elements and electronic circuits.
Software tools for electrical engineering use may be grouped into categories according to function. Two categories are 1) circuit element modeling tools and 2) circuit design and simulation tools. Circuit element modeling tools are used to characterize a particular circuit element and create a software model for subsequent use in a circuit design and simulation program.
A model is a mathematical representation (or other type of representation) of a real world physical device (RWPD) that predicts the behavior of the real world physical device when provided with a controlled set of inputs.
Two types of models used in engineering are analytical models and numerical models. Analytical models are mathematical representations of RWPDs where a limited set of equations are used to represent a RWPD. Numerical models generally attempt to represent RWPDs by solving a more fundamental, or more physical set of equations. This often requires the solution of a large set of simultaneous equations which are restatements of a fundamental equation at different spatial or time coordinates. It will be sufficient to define a numerical model as one that requires the solution of many simultaneous equations, many more than analytical models use.
Modeling is the process of creating a model that is representative of the structure, behavior, operation, or other property of a real world physical device. Models may have other models as components, e.g. circuit models may have circuit element models.
Modeling tools use a variety of techniques to arrive at a model for a particular element, often called a device model. For example, an inductor can be modeled using commercially available software that provides a user with element parameters such as inductance and resistance for a particular geometry of the element. The modeling software can also provide element parameters over frequency in a variety of graphic or tabular formats.
Once a model is created for a circuit element, a circuit designer uses the device model in a circuit design and simulation tool, where the model is combined with other circuit element models (other device models) to form a complete circuit model. The complete circuit is then simulated using the simulation tool. The simulation tool provides a designer with circuit performance data.
Circuit designers need access to fast circuit design/simulation tools due to the iterative nature of the design process and short design cycles. Current circuit simulations often take hours or more to run. However, the preprocessing stage for the individual components, or RWPDs, usually takes much less time because less accurate analytic models are used in the interest of saving time. The time spent preprocessing is important, as this is time that the circuit designer must sit and wait at his/her terminal. To compete, the more accurate, and hence more desirable, numerical models must take no more than mere seconds, or occasionally, minutes to run. A variety of closed-form analytic models for on-chip inductors (spiral, square, etc.) can be found for the inductance, series resistance, capacitances and substrate coupling of the inductors. Since these models are only approximate models, they must be fitted (tuned) to correlate with measured data of the RWPD that spans the entire design space (the range of design variables used in the model) in order to validate and verify the model.
Model validation/verification is essentially the process of determining the degree of similarity between the model and the RWPD via comparison of measurements of the RWPD with simulation results to the same set of known(and controlled) inputs.
Factors contributing to the difficulty of this tuning process include a large variety of device types for a given circuit element (for example, inductive elements include inductors, center-tapped inductors, transformers, baluns, etc.), a broad range of parameters (design space), and widely varying process technologies. For example, in order to maximize the quality factor Q, of an inductor, the conductor line width (w) and thickness (t) become so large, one cannot make the assumption that the current density in the conductor is uniform. This non-uniform current density, (partly due to skin and/or proximity phenomena), has the effect of lowering the inductance of an inductive element by a small but often significant amount, especially in high frequency applications. Further, the non-uniform current density also has the effect of increasing the AC resistance of the inductive element. All these parameters, w, t, Q, inductance, current density, AC resistance, and more, exacerbate the modeling/tuning process.
A model created for predicting the characteristics of a circuit element should be as accurate as possible (robust). If a circuit element is not properly modeled, and a circuit is designed using that model, the circuit may not meet specifications, or perhaps, not function at all.
To further tax the robustness of analytic models, technologies using two layers of thick metal for inductors and transformers are now being considered. For example, the skin effect in a two layer, thick-metal process is more complex to model because the current in each layer will tend to crowd toward only one surface (the surface farthest from the other layer) instead of both top and bottom surfaces as in a single-layer-thick-metal process.
One motivation for desiring to employ numerical models in circuit simulation and circuit element characterization is the high level of robustness and accuracy over the entire design space that can be achieved, which is often within about 1%.
However, it is well known that numerical modeling of circuits and/or circuit elements is too slow to be of practical use in a circuit design environment. In fact, a detailed numerical model of a circuit element takes a computer many hours to obtain a solution. Long solution times are often the result of having to solve a large matrix equation. Further, many matrix operations, such as inverting a large matrix, take a very long time for even a computer to perform. Very powerful, fast computers are available to perform such calculations at a quicker pace, but they are prohibitively expensive to put on every circuit designer""s desk, or even to put one in every design center.
To solve the aforementioned problems and others, it is desirable to have an accurate numerical model for inductive circuit elements contained within a circuit design environment such that it is fast enough that the circuit simulation setup time is not significantly increased, or preferably, not increased at all.
Embodiments of the invention herein include numerical modeling methods that reduces prior art device model simulation time by as much as a factor of about 3000 when simulating inductive circuit elements. Accuracies of about 1% may be achieved in as little time as about a second for a single frequency point using embodiments of the present invention.
One concept of embodiments of the present invention herein, is the applicant""s recognition that the impedance matrix for an inductive circuit element has certain unique characteristics that in turn allow Strassen""s method of inverting a matrix to be applied to the impedance matrix for an inductive element.
Further, Strassen""s method to invert a matrix is modified such that not all of Strassen""s steps need be performed to successfully invert the impedance matrix for an inductive circuit element, including, but not limited to, circular and square spiral inductors.
Another concept of the inventive method herein is to recognize that the geometry of some inductive elements are highly symmetric about a horizontal plane, thereby allowing the number of equations to be solved to be reduced by a factor of two. This is possible in these cases because the current distribution in one half of the structure is substantially the same as the current distribution in the other half of the structure that is on the other side of the plane of symmetry. Consequently, the current distribution in the entire structure may be calculated by solving a system of equations (e.g. matrix equation) with only half the number of unknowns to obtain the total inductance and resistance.
The applicant also recognizes conductors often have non-uniform current densities, such as when the skin effect is prominent at higher frequencies. This phenomenon is exploited by embodiments of the invention herein by reducing the number of equations to be solved. This is accomplished by dividing the inductive circuit element into many individual sections, where the sections in the center are larger than the sections at the edges of the conductor where the current is more concentrated and variable due to factors such as skin effect and/or proximity effects.
The overall reduction in modeling time resulting from the inventive methods herein, while still providing very high accuracy, enables circuit element (device)modeling capability to be provided within the same tool as circuit simulation software without suffering long solution times.
Using embodiments of the invention herein a circuit designer may now investigate secondary effects that have been modeled previously only by modelers using different simulation tools outside the circuit design-simulation environment. For example, the effects of variable-width spiral inductors, the effect of placing an AC bias on the inside inductor lead, or on the outside inductor lead, may now be analyzed directly by the circuit designer. Another example is the effect of continuous vias between two layers of metal used in parallel.
Secondly, tuning (tuning is the process of adjusting parameter values to make the model agree with measurements of a RWPD) to a new process would be nearly, and in some cases, totally eliminated.
Model simulation time of a particular RWPD using an embodiment of the invention herein, was reduced from 1 hour to less than 3 seconds, an overall savings in computational time of  greater than 99.9%.
It is an object of embodiments of the present invention to provide a method of very quickly inverting an impedance matrix representative of an inductive element, or group of elements.
It is another object of embodiments of the present invention to provide a method of very quickly inverting an impedance matrix representative of an inductive element, where the method is embodied in a circuit element modeling tool.
It is another object of embodiments of the present invention to provide a method of very quickly inverting an impedance matrix representative of an inductive element where the method is a modified and shortened version of Strassens""s method.
It is another object of embodiments of the present invention to provide a method of very quickly inverting an impedance matrix representative of an inductive element, where the method is embodied in a circuit simulation tool.
It is another object of embodiments of the present invention to provide a circuit simulation tool that aids an operator in modeling an inductive circuit element, and further, aids an operator in simulating a circuit using the inventive numerical model.
This and other advantages and uses of the invention herein will be apparent to one of ordinary skill in the art upon reading the teaching herein.